PROF. BELYAVSKY. Theory of Sound as Applied to Music. State Publishing House, 1925, pp. 239. Price 5 rubles.

The book was conceived by the author very broadly, with a view both to students of musical educational institutions and to persons studying acoustics in general. For the former, however, the material gathered in the book is too extensive, abounding in an excessively large number of details taken from general courses in physics, and therefore the book is not very suitable as a textbook for musical education. On the other hand, with respect to musical acoustics, the material is insufficient: the little that is directly important in acoustics for music and that has been developed only in recent years has not entered the book.

For the latter, i.e., for persons studying acoustics in general, the book provides comparatively little of value, since the literary material collected by the author is greatly out of date. Among the large number of books listed in the bibliographical index, we do not find books more recent than the beginning of our century, while contemporary literature is not cited at all. The numerous and fundamental works of the last two decades concerning the study of speech sounds and musical instruments, the study of consonances and combination tones, and works on the physics and physiology of hearing, which have placed all these questions on a firm scientific foundation, are completely untouched by the author. Important questions of architectural acoustics are likewise not covered. Needless to say, questions of transmitting speech and music by wires and radio, which in our time arouse broad interest, are not touched upon at all, unless one counts the outdated information on the singing arc, the telephone, and the phonograph. Modern acoustics has undergone such rapid growth and deepening that the section of it dealing with musical sounds inevitably ought to have been presented more up to date in 1925.

The chapter on musical temperaments and scales has been compiled by the author very interestingly and fully.

The book contains a number of lapses and errors:

P. 11, 3rd paragraph. It is incorrectly stated that reflection at the boundary of a medium with a lower speed of sound occurs with a change of sign, while at the boundary of a medium with a higher speed it occurs without a change of sign. This is probably a slip, and should be understood the other way round. But the point is that this, too, would be incorrect: the reflection of one or another tone is determined not only by the speed of sound, but by the product of the speed of sound and the density, or by the acoustic stiffness of the medium.

P. 41, paragraph 3, and p. 43, paragraph 2. The old data given on the sensitivity of the ear should be corrected.

P. 49, paragraph 5. The amplification of the sound of a tuning fork placed on a resonance board or table is incorrectly explained by an increase in the number of waves reaching the ear.

P. 50, fig. 74. The drawing is incorrect. In Kundt’s experiment, in a tube with gas, a node forms both at the closed end and at the end of the sounding rod (almost exactly).

p. 62, paragraph 2 from the bottom. The definition of acoustic consonance as combinations of tones with a ratio of numbers of vibrations expressed by numbers from 1 to 6 is quite unacceptable. The intervals \(7:4\) or \(7:6\), from the acoustic point of view, are no worse a consonance than the interval \(6:5\) (the minor third).

p. 134, paragraph 4. The assertion that the combination tones of vowels are not harmonic is too bold. The observations of Hermann, proving the possibility of the appearance of non-harmonic overtones, have not been confirmed by later investigators.

p. 142, lines 7–6 from the bottom. It is stated that, in the sound of a violin, the amplitude of vibration and the sound intensity of the second overtone amount to \(\frac{1}{4}\) of the same quantities for the fundamental tone, \(\frac{1}{9}\) for the third, and \(\frac{1}{16}\) for the fourth overtone. As regards the decrease in the amplitude of the string—this is correct, according to Helmholtz’s calculations. But the sound intensity of the overtones decreases in the ratio

\[ 1:\frac{1}{16}:\frac{1}{81}:\frac{1}{256}. \]

p. 160, paragraph 2. It is incorrectly stated that the lungs are supported from below by the thoraco-abdominal diaphragm.

p. 161, paragraph 6. The assertion that the role of the oral cavity as a resonator is insignificant is completely incomprehensible.

p. 165, paragraph 6. Helmholtz’s theory of vowel formation is presented in an overly categorical form. Helmholtz does not consider that the characteristic tone of a vowel—the formant, according to Hermann—is a “quite definite and constant” tone. Helmholtz indicates that this tone changes slightly depending on the shade of the vowels in different dialects and among different persons.

S. Rzhevkin.